Physical Oceanography, Vol. 15, No. 5, 2005
TRANSPORT OF SEDIMENTS ENTRAPPED BY TOPOGRAPHIC WAVES
A. A. Slepyshev
In the Boussinesq approximation, for topographic waves entrapped by a sloping bottom, we de-
termine mean currents induced by a wave due to nonlinearity with regard for turbulent viscosity
and diffusion. We determine the thickness of the bottom boundary layer, the vertical turbulent
exchange coefficients, and turbulent stresses on the upper boundary of the boundary layer de-
pending on the parameters of the wave. In the diffusion approximation, we find the vertical dis-
tribution of the concentration of sediments suspended by the wave and the flow rates of sedi-
ments along and perpendicular to the isobaths.
The investigation of dynamic processes near the bottom becomes especially urgent due to the phenomena
suspension and transport of bottom sediments in the shelf zone. Wind waves play an important role in the accu-
mulation and washout of sediments directly in the coastal zone of the sea. The influence of surface waves is ob-
served down to depths equal to a half of the wavelength . At large depths, the influence of internal and topo-
graphic waves is predominant. The topographic waves entrapped by the sloping bottom whose energy is con-
centrated near the bottom exert active influence on the bottom. In the bottom layer of the sea, over the shelf and
continental slope, there exists an important class of topographic Kelvin-type waves for which the component of
the wave orbital velocity normal to the bottom is equal to zero [2–6].
If the turbulent tangential stresses formed near the bottom are higher than the critical values corresponding
to the onset of motion of the sediments, then the wave stirs up bottom sediments and performs their horizontal
transport (realized by mean currents induced by the bottom topographic waves).
In this connection, the problem of determination of mean currents induced by topographic waves entrapped
by the sloping bottom due to nonlinear effects in the presence of turbulent viscosity and diffusion over an arbit-
rarily oriented slope seems to be quite urgent. The original nonlinear equations of hydrodynamics for wave dis-
turbances are solved in a weakly nonlinear approximation by the perturbation method [7, 8]. In the first order of
smallness in the wave amplitude, we determine the solution of the linear approximation and the dispersion rela-
tion. In the second order of smallness, we determine mean currents induced by the waves after averaging of the
original equations over the wave period. In the present work, the turbulent-exchange coefficients depend on the
distance from the bottom. It is supposed that, above the bottom layer whose thickness is determined by the par-
ameters of waves, the coefficients of turbulent viscosity and diffusion are regarded as constant and equal to their
values on the upper boundary of the bottom layer. The vertical (along the
z-axis) distribution of the turbulent-
exchange coefficients in the bottom layer is determined in what follows.
We write the system of hydrodynamic equations for wave disturbances in a coordinate system whose
plane coincides with the plane of the bottom. The
x-axis is parallel to the free nondisturbed sea surface and
makes an angle β with the westward direction and the
z-axis coincides with direction of the outer normal. The
angle β is regarded as positive if it is obtained by a counterclockwise rotation of a parallel to the
vector of the angular velocity of Earth’s rotation has the following projections onto the
Marine Hydrophysical Institute, Ukrainian Academy of Sciences, Sevastopol.
Translated from Morskoi Gidrofizicheskii Zhurnal, No.
13–24, September–October, 2005. Original article submitted November
19, 2003; revision submitted June 16, 2004.
0928-5105/05/1505–0275 © 2005 Springer Science+Business Media, Inc. 275